we have that
[√(2x+1)]+3=0
for x=4
[√(2*4+1)]+3=0
[√(9)]+3=0
3+3=0----------6 is not zero
therefore
the solution is not correct for x=4
[√(2x+1)]+3=0--------> [√(2x+1)]=-3---------> There is no real solution for that equation
Because (2x+1) >= 0
the solution is with complex numbers
